Finite Group Databasebeta

D47×#2048 #26244104

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productD47×#2048

Splittings

FittingC47×#2048 ⋊ C2
SylowC47 ⋊ C2×#2048

Subgroups

subgroupG/H
centerC2#394×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2048C2
socleC2×C47C2×#394
prime radicalC2×AGL(1,ℤ/8)×D47C2
hypercenter#2048D47
hypocenterC47C2×#2048
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2048

1450 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

575 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 197394);